Missions are given by your Sponsor. Either he will send you a Pigeon Mail requesting you to do a mission, or you can go to your sponsor and request for him to give you one. You can either reject the mission or accept it.
How to Find your Sponsor
Everyone's sponsors are different. Find out where yours is located by going onto your map and spotting the large 'S' sign. Click on it, and there will be an arrow that guides you. Finding a location Click here to learn more about finding a location
Once there, you will see an apartment manager with a huge orange arrow above his head:
When you talk to your Sponsor regarding a mission, he will give you a hint on what the mission will be about. He will give you the name of the person you are to help and the directions to meet that person on the map.